Pointwise strong approximation of almost periodic functions in S^1

TL;DR

This paper investigates how well almost periodic functions in S^1 can be approximated pointwise using matrix means of their Fourier series partial sums, providing new insights into their approximation behavior.

Contribution

It introduces a new approach to pointwise approximation of S^1 almost periodic functions using matrix means, expanding understanding of their convergence properties.

Findings

Established bounds for deviations in strong mean approximations

Demonstrated effectiveness of matrix means in approximating almost periodic functions

Extended classical approximation results to the S^1 almost periodic setting

Abstract

We consider the class GM(2b) in pointwise estimate of the deviations in strong mean of S^1 almost periodic functions from matrix means of partial sums of their Fourier series.